




'''simple docstring'''







import unittest

import numpy as np







def 						_A      ( UpperCAmelCase      ,UpperCAmelCase      ,UpperCAmelCase      ,UpperCAmelCase = None      ,):






   '''simple docstring'''







   A__       =     np.shape(UpperCAmelCase						)
   A__       =     np.shape(UpperCAmelCase						)
   A__       =     np.shape(UpperCAmelCase						)

   if shape_a[0] != shape_b[0]:
      A__       =     (
          'Expected the same number of rows for A and B. '
          F"""Instead found A of size {shape_a} and B of size {shape_b}"""
      )
      raise ValueError(UpperCAmelCase						)

   if shape_b[1] != shape_c[1]:
      A__       =     (
          'Expected the same number of columns for B and C. '
          F"""Instead found B of size {shape_b} and C of size {shape_c}"""
      )
      raise ValueError(UpperCAmelCase						)

   A__       =     pseudo_inv
   if a_inv is None:
      try:
         A__       =     np.linalg.inv(UpperCAmelCase						)
      except np.linalg.LinAlgError:
         raise ValueError(
             'Input matrix A is not invertible. Cannot compute Schur complement.'						)

   return mat_c - mat_b.T @ a_inv @ mat_b

class 	_snake_case(			unittest.TestCase      ):






 def 						_UpperCamelCase (self       :  str    )       ->   None:






    """simple docstring"""


    A__       =     np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]    )
    A__       =     np.array([[0, 3], [3, 0], [2, 3]]    )
    A__       =     np.array([[2, 1], [6, 3]]    )

    A__       =     schur_complement(a    ,		a    ,		a    )

    A__       =     np.block([[a, b], [b.T, c]]    )

    A__       =     np.linalg.det(a    )
    A__       =     np.linalg.det(a    )
    A__       =     np.linalg.det(a    )

    self.assertAlmostEqual(a    ,		det_a * det_s    )






 def 						_UpperCamelCase (self       :  Dict    )       ->   None:






    """simple docstring"""


    A__       =     np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]    )
    A__       =     np.array([[0, 3], [3, 0], [2, 3]]    )
    A__       =     np.array([[2, 1], [6, 3]]    )

    with self.assertRaises(a    ):
       schur_complement(a    ,		a    ,		a    )






 def 						_UpperCamelCase (self       :  str    )       ->   None:






    """simple docstring"""


    A__       =     np.array([[1, 2, 1], [2, 1, 2], [3, 2, 4]]    )
    A__       =     np.array([[0, 3], [3, 0], [2, 3]]    )
    A__       =     np.array([[2, 1, 3], [6, 3, 5]]    )

    with self.assertRaises(a    ):
       schur_complement(a    ,		a    ,		a    )


if __name__ == "__main__":
    import doctest

    doctest.testmod()
    unittest.main()








'''simple docstring'''







from dataclasses import dataclass
from typing import List, Optional, Union

import numpy as np
import PIL

from ...utils import BaseOutput, OptionalDependencyNotAvailable, is_torch_available, is_transformers_available
from .timesteps import (
    fastaa_timesteps,
    smartaa_timesteps,
    smartaa_timesteps,
    smartaaa_timesteps,
    smartaaa_timesteps,
    superaa_timesteps,
    superaa_timesteps,
    superaaa_timesteps,
)

@dataclass
class 	_snake_case(			UpperCAmelCase      ):
 __snake_case:							Union[List[PIL.Image.Image], np.ndarray]
 __snake_case:							Optional[List[bool]]
 __snake_case:							Optional[List[bool]]


try:
    if not (is_transformers_available() and is_torch_available()):
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    from ...utils.dummy_torch_and_transformers_objects import *  # noqa F403
else:
    from .pipeline_if import IFPipeline
    from .pipeline_if_imgaimg import IFImgaImgPipeline
    from .pipeline_if_imgaimg_superresolution import IFImgaImgSuperResolutionPipeline
    from .pipeline_if_inpainting import IFInpaintingPipeline
    from .pipeline_if_inpainting_superresolution import IFInpaintingSuperResolutionPipeline
    from .pipeline_if_superresolution import IFSuperResolutionPipeline
    from .safety_checker import IFSafetyChecker
    from .watermark import IFWatermarker


